Comparative Study Of Image Inpainting Models Based On Fractional Derivatives And Non-local Total Variatio

Firstly,an augmented Lagrangian algorithm for solving the fractional total variation(FOTV)image inpainting model and the fractional q-Laplace(0<q<1)total variation image inpainting model are proposed in this paper.In the process of derivation of the two algorithms,the two models are converted into the sequences of u subproblems,p subproblems and the update step of Lagrangian multipliers for solving.The u subproblem derived from both models can be solved using the fast Fourier transform(FFT).The p subproblem derived from the first model can be solved directly using the Shrinkage operator,while the p subproblem derived from the second model can be solved using the alternating direction method.Secondly,according to the framework of the split Bregman algorithm for solving the non-local total variation(NLTV)image inpainting model proposed by predecessors,the specific steps of the algorithm are derived in detail.In this process,the original problem is decomposed into u subproblem,d subproblem and Bregman variable update step to solve.The u subproblem can be solved by calculating Euler-Lagrange equation and adopting Gauss-Seidel iteration,the d subproblem can be solved by Shrinkage operator.We give the discrete formula of this algorithm.Finally,two kinds of parameter optimization methods the two algorithms are proposed in this paper,numerical implementation on three test images are given.Then they are compared with the experimental results of the split Bregman algorithm of the NLTV image inpainting model and the gradient descent algorithm of classic TV image inpainting model on the same images.The experimental results show that the augmented Lagrangian algorithm for solving the fractional q-Laplace total variation image inpainting model can achieve better inpainting effect than the other algorithms in this paper with proper parameter selection.